Public key depends on high level math. That math has some asymetric
property that we can use to achieve the public-private key relationships.

The problem is that the discovery of smarter math can invalidate the
asymetry and make it more symetrical. This has to do with P=NP, which is
also less trivial than a first explaination makes it seem. If it becomes
even effectively symetrical (P is that) it will stop having the nice
useable property.

Symetric cryptography does a much easier thing. It combines data and some
mysterious data (key) in a way that you cannot extract data without the
mysterious data from the result. It's like a + b = c. Given c you need b to
find a. The tricks that are involved are mostly about sufficiently mixing
data, to make sure there's enough possible b's to never guess it correctly
and that all those b's have the same chance of being the one b. Preferably
even when you have both A and C, but that's really hard.

So I'd say Bruce said that in an effort to move to more well understood
cryptography. It is also a way to move people towards simply better
algorithms, as most public key systems are very, very bad.
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